Basic Math Examples

$43 \frac{1}{21} - 27 \frac{5}{14}$

Step 1

Convert

$43 \frac{1}{21}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$43 + \frac{1}{21} - 27 \frac{5}{14}$

Step 1.2

Add

$43$ and

$\frac{1}{21}$ .

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Step 1.2.1

To write

$43$ as a fraction with a common denominator, multiply by

$\frac{21}{21}$ .

$43 \cdot \frac{21}{21} + \frac{1}{21} - 27 \frac{5}{14}$

Step 1.2.2

Combine

$43$ and

$\frac{21}{21}$ .

$\frac{43 \cdot 21}{21} + \frac{1}{21} - 27 \frac{5}{14}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{43 \cdot 21 + 1}{21} - 27 \frac{5}{14}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$43$ by

$21$ .

$\frac{903 + 1}{21} - 27 \frac{5}{14}$

Step 1.2.4.2

Add

$903$ and

$1$ .

$\frac{904}{21} - 27 \frac{5}{14}$

Step 2

Convert

$27 \frac{5}{14}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{904}{21} - (27 + \frac{5}{14})$

Step 2.2

Add

$27$ and

$\frac{5}{14}$ .

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Step 2.2.1

To write

$27$ as a fraction with a common denominator, multiply by

$\frac{14}{14}$ .

$\frac{904}{21} - (27 \cdot \frac{14}{14} + \frac{5}{14})$

Step 2.2.2

Combine

$27$ and

$\frac{14}{14}$ .

$\frac{904}{21} - (\frac{27 \cdot 14}{14} + \frac{5}{14})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{904}{21} - \frac{27 \cdot 14 + 5}{14}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$27$ by

$14$ .

$\frac{904}{21} - \frac{378 + 5}{14}$

Step 2.2.4.2

Add

$378$ and

$5$ .

$\frac{904}{21} - \frac{383}{14}$

Step 3

To write

$\frac{904}{21}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{904}{21} \cdot \frac{2}{2} - \frac{383}{14}$

Step 4

To write

$- \frac{383}{14}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{904}{21} \cdot \frac{2}{2} - \frac{383}{14} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

$42$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{904}{21}$ by

$\frac{2}{2}$ .

$\frac{904 \cdot 2}{21 \cdot 2} - \frac{383}{14} \cdot \frac{3}{3}$

Step 5.2

Multiply

$21$ by

$2$ .

$\frac{904 \cdot 2}{42} - \frac{383}{14} \cdot \frac{3}{3}$

Step 5.3

Multiply

$\frac{383}{14}$ by

$\frac{3}{3}$ .

$\frac{904 \cdot 2}{42} - \frac{383 \cdot 3}{14 \cdot 3}$

Step 5.4

Multiply

$14$ by

$3$ .

$\frac{904 \cdot 2}{42} - \frac{383 \cdot 3}{42}$

Step 6

Combine the numerators over the common denominator.

$\frac{904 \cdot 2 - 383 \cdot 3}{42}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$904$ by

$2$ .

$\frac{1808 - 383 \cdot 3}{42}$

Step 7.2

Multiply

$- 383$ by

$3$ .

$\frac{1808 - 1149}{42}$

Step 7.3

Subtract

$1149$ from

$1808$ .

$\frac{659}{42}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{659}{42}$

Decimal Form:

$15.69047619 \dots$

Mixed Number Form:

$15 \frac{29}{42}$